Question

How do you differentiate `x^4(x+y)=y^2(3x-y)`?

Answer 1

First, use the distributive property to write `x^5+x^4y=3xy^2-y^3`.

Next, make the assumption that `y` is a function of `x` and differentiate both sides with respect to `x`, using the Product Rule and Chain Rule as necessary:

`5x^4+4x^3y+x^4 dy/dx=3y^2+6x y dy/dx-3y^2 dy/dx`

Finally, solve for `dy/dx`:

`dy/dx(x^4-6xy+3y^2)=-5x^4-4x^3y+3y^2`

`dy/dx=\frac{-5x^4-4x^3y+3y^2}{x^4-6xy+3y^2}`